Computing geodesic spectra of surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Conformal spherical representation of 3D genus-zero meshes
Pattern Recognition
High Resolution Tracking of Non-Rigid Motion of Densely Sampled 3D Data Using Harmonic Maps
International Journal of Computer Vision
Parametric polynomial minimal surfaces of degree six with isothermal parameter
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Discrete complex structure on surfel surfaces
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
2D-shape analysis using conformal mapping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
New 3d fourier descriptors for genus-zero mesh objects
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Discrete conformal shape representation and reconstruction of 3d mesh objects
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Tracking by detection for interactive image augmentation in laparoscopy
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
Deformation similarity measurement in quasi-conformal shape space
Graphical Models
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3D surface classification is a fundamental problem incomputer vision and computational geometry. Surfaces canbe classified by different transformation groups. Traditionalclassification methods mainly use topological transformationgroups and Euclidean transformation groups. This paperintroduces a novel method to classify surfaces by conformaltransformation groups. Conformal equivalent classis refiner than topological equivalent class and coarser thanisometric equivalent class, making it suitable for practicalclassification purposes. For general surfaces, the gradientfields of conformal maps form a vector space, which hasa natural structure invariant under conformal transformations.We present an algorithm to compute this conformalstructure, which can be represented as matrices, and use itto classify surfaces. The result is intrinsic to the geometry,invariant to triangulation and insensitive to resolution. Tothe best of our knowledge, this is the first paper to classifysurfaces with arbitrary topologies by global conformal invariants.The method introduced here can also be used forsurface matching problems.